One end of a spring of force constant K is fixed to a vertical wall and the other to a body of mass m resting on a smooth horizontal surface. There is another wall at a distance $$x0$$ from the body. The spring is then compressed by $$3x0$$ and released. The time taken to strike the wall from the instant of release is (given$$ $$sin$$$$-1(l/3) $$=$$ $$($$π$$/9))$$

Question

One end of a spring of force constant K is fixed to a vertical wall and the other to a body of mass m resting on a smooth horizontal surface. There is another wall at a distance $$x0$$ from the body. The spring is then compressed by $$3x0$$ and released. The time taken to strike the wall from the instant of release is (given$$ $$sin$$$$-1(l/3) $$=$$ $$($$π$$/9))$$

Infinity Learn · Accepted Answer

When spring is compressed by $$3x0$$. Amplitude, $$A=3x0$$. The time taken from extreme compressed position to mean position, $$t1=T/4$$. If time taken (t2) from mean position to $$x=x0$$ is given $$byx=A$$ $$sin2$$$$π$$$$t2T$$     ⇒        $$x0=3x0$$ $$sin$$ $$2$$$$π$$$$t2T$$ $$sin$$ $$2$$$$π$$$$t2T=13$$      ⇒     $$2$$$$π$$$$t2T=$$π$$9$$     ⇒ $$t2=T18$$ $$t1+t2$$ $$=T4+T18=1118T$$          $$=1182$$$$π$$$$mK=119$$$$π$$mK

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